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LINKTV
Feb 13, 2013 4:30pm PST
different kinds of tilings that involve other kinds of shapes. when you have a pentagon, for example, and you try to imagine tiling it so that it goes to infinity, in effect, you find that you get gaps between the pentagons. you can't tile them evenly on a flat surface, so you have to put it on this kind of surface here. and you can show it in a picture by distorting the shape, by making them smaller as you go further and further out. and so, in principle, these will get really, really tiny as you get further and further out. and you in effect go to infinity at the very edge here. now, this is just a representation of what that kind of surface would be like. it's something called a hyperbolic plane. now, this remarkable sculpture done by someone named helaman ferguson, who is both a mathematician and an artist, this brings tother a lot of different aspects of infinity all in one piece. if you look at this sculpture, the cross-section is a triangle with the sides bent inward, and what's happened is that this triangle turns and twists around and then joins back up again. so it has a twist i
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